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3 years ago

Solve 10e^2x - 5 =23^x for x.

Mathematics

2 answers:

yawa3891 [41]3 years ago

5 0

$10e^{2x}-5=23e^x\qquad\text{subtract}\ 23e^x\ \text{from both sides}\\\\10e^{2x}-23e^x-5=0\\\\10(e^x)^2-23(e^x)-5=0\\\\\text{substitution:}\ e^x=t > 0\\\\10t^2-23t-5=0\\\\10t^2-25t+2t-5=0\\\\5t(2t-5)+1(2t-5)=0\\\\(2t-5)(5t+1)=0\iff2t-5=0\ \vee\ 5t+1=0\\\\2t=5\ \vee\ 5t=-1\\\\t=\dfrac{5}{2} > 0\ \vee\ t=-\dfrac{1}{5} < 0\\\\\text{therefore}\ e^x=\dfrac{5}{2}\to\ln e^x=\ln\left(\dfrac{5}{2}\right)\\\\\boxed{x=\ln\left(\dfrac{5}{2}\right)}$

bixtya [17]3 years ago

5 0

Answer:

B is the correct option choice !

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3 years ago

What is the answer for Jessica is making two loaves of banana bread she needs 3/4 of sugar for each lol her measuring cup can on

Rudiy27

Answer: 6

Step-by-step explanation:

1/4 times 3 = 3/4 times 2= 6/4 enough for two loaves.

Mark me as brainliest if this helps!

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3 years ago

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I am confused on this question

kaheart [24]

<h3>Answer: Around 4681 grills</h3>

============================================

Explanation:

x = number of years

y = number of grills sold

The equation we'll use is the exponential equation $y = 3300(1.06)^x$

The 3300 of course is the initial amount sold. The 1.06 as the base indicates that the sales increase by 6% each year. Think of it the 1.06 as 1+0.06 = 100% + 6%

If we plugged x = 0 into that equation, then we get

$y = 3300(1.06)^x = 3300(1.06)^0 = 3300$

which helps confirm the correct equation.

----------------

Now plug in x = 6 to find the sales for year 6.

$y = 3300(1.06)^x = 3300(1.06)^6 \approx 4681.11 \approx 4681$

The projected sales for year 6 are about 4681 grills. This is an estimate based on the assumption that the sales will increase by 6% each year. Of course, the reality is that things aren't always so simple like this (but it should give a fairly good idea of what's going on).

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2 years ago

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pishuonlain [190]

Answer:
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Step-by-Step equation:

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3 years ago

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